(mathematics) The matrix of the coefficients, together with the constant terms, in a system of linear equations.
| Sci-Tech Dictionary: augmented matrix |
(mathematics) The matrix of the coefficients, together with the constant terms, in a system of linear equations.
| 5min Related Video: Augmented matrix |
| Wikipedia: Augmented matrix |
In linear algebra, the augmented matrix of a matrix is obtained by changing a matrix in some way.
Given the matrices A and B, where:

Then, the augmented matrix (A|B) is written as:
![(A|B)=
\left[\begin{array}{ccc|c}
1 & 3 & 2 & 4 \\
2 & 0 & 1 & 3 \\
5 & 2 & 2 & 1
\end{array}\right].](http://wpcontent.answers.com/math/9/0/b/90bb313a8261f5819bbd627527a4fe68.png)
This is useful when solving systems of linear equations or the augmented matrix may also be used to find the inverse of a matrix by combining it with the identity matrix.
Let C be a square 2×2 matrix where 
To find the inverse of C we create (C|I) where I is the 2×2 identity matrix. We then reduce the part of (C|I) corresponding to C to the identity matrix using only elementary matrix transformations on (C|I).
![(C|I) =
\left[\begin{array}{cc|cc}
1 & 3 & 1 & 0\\
-5 & 0 & 0 & 1
\end{array}\right]](http://wpcontent.answers.com/math/2/2/8/2287af9b77a63d0c27d9d220fda56960.png)
![(I|C^{-1}) =
\left[\begin{array}{cc|cc}
1 & 0 & 0 & -\frac{1}{5} \\
0 & 1 & \frac{1}{3} & \frac{1}{15}
\end{array}\right]](http://wpcontent.answers.com/math/7/2/c/72cb9fd6adf4343b3c37567082e59ddf.png)
As used in linear algebra, an augmented matrix is used to represent the coefficients and the solution vector of each equation set. For the set of equations:

the augmented matrix would be composed of

Leaving us with:
or
![(A|B) =
\left[\begin{array}{ccc|c}
1 & 0 & 0 & 4 \\
0 & 1 & 0 & 1 \\
0 & 0 & 1 & -2 \\
\end{array}\right].](http://wpcontent.answers.com/math/b/5/1/b51f8bb10b587ca9409f15ea256ad5ae.png)
| This algebra-related article is a stub. You can help Wikipedia by expanding it. |
This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)
| Row echelon form | |
| Indeterminate system | |
| Montante's method |
Copyrights:
![]() | Sci-Tech Dictionary. McGraw-Hill Dictionary of Scientific and Technical Terms. Copyright © 2003, 1994, 1989, 1984, 1978, 1976, 1974 by McGraw-Hill Companies, Inc. All rights reserved. Read more | |
![]() | Wikipedia. This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article "Augmented matrix". Read more |